Question

A parallel plate capacitor of plate area $A$ has a charge $Q$. The force on each plate of the capacitor is

• A. $\frac{2Q^2}{{\epsilon }_{0}A}$
• B. $\frac{Q^2}{{\epsilon }_{0}A}$
• C. $\frac{Q^2}{2{\epsilon }_{0}A}$
• D. Zero

Answer 1

Answer: (C)

Force on one plate due to another is
$F=QE=Q\times \frac{\sigma }{2{\epsilon }_0}$
$=Q\left[\frac{Q}{2A{\epsilon }_0}\right]$
$=\frac{Q^2}{2A{\epsilon }_0}$